Lecture 7: A short introduction to regression

Describing associations

Measures of associations

  • A common goal in statistical analysis is to describe associations
  • Statistics are full of specific methods to describe and test for statistical associations
    • E.g. t-test, ANOVA, ANCOVA, Pearson’s correlation, Spearman’s correlation, Chi Square test, etc.
  • Most of the commonly used methods can be re-framed as regression models

Difference between two groups in outcome, or the association between group and outcome

\(\text{Outcome} = \beta_0 + \beta_1 \times \text{Group}_{\text{B}}\)

Where
\(\text{Group}_{\text{B}} = 1\) when group==B
\(\text{Group}_{\text{B}} = 0\) when group==A

Association between height and VO2max

For every 1-unit increase in height, the outcome increase by \(\beta_1\) units.

\(\text{Outcome} = \beta_0 + \beta_1 \times \text{Height}\)

A two dimensional system